# PTAH inequality result

There is an additional classic inequality^{} to be added to the list (A) through (F), namely the maximum-entropy inequality (in logarithmic form)

$$-\sum _{i=1}^{n}{p}_{i}\mathrm{log}{p}_{i}\le \mathrm{log}n.$$ |

Also, inequality (C) should be labeled “the Kullback–Leibler inequality”.

Then, the labeling could be modified: the first time the PTAH inequality appears it could be labeled (P);
then the maximum-entropy inequality could be labeled (G), followed by Hölder’s inequality (already labeled (H));
and the statement could be “the inequalities (A) through (G) are equivalent^{}, each is a special case of (H),
and (H) is a special case of (P). However, it appears that none of the reverse implications^{} hold.”

Title | PTAH inequality result |
---|---|

Canonical name | PTAHInequalityResult |

Date of creation | 2013-03-22 18:08:33 |

Last modified on | 2013-03-22 18:08:33 |

Owner | cappymate (20671) |

Last modified by | cappymate (20671) |

Numerical id | 4 |

Author | cappymate (20671) |

Entry type | Result |

Classification | msc 26D15 |